Related papers: Fully Bayesian Penalized Regression with a General…
In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
Penalized regression has become a standard tool for model building across a wide range of application domains. Common practice is to tune the amount of penalization to tradeoff bias and variance or to optimize some other measure of…
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference,…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
The paper deals with generalized functional regression. The aim is to estimate the influence of covariates on observations, drawn from an exponential distribution. The link considered has a semiparametric expression: if we are interested in…
The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…
Motivation: Recent advances in technology for brain imaging and high-throughput genotyping have motivated studies examining the influence of genetic variation on brain structure. Wang et al. (Bioinformatics, 2012) have developed an approach…
In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…
We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…
We introduce a novel function-on-function linear quantile regression model to characterize the entire conditional distribution of a functional response for a given functional predictor. Tensor cubic $B$-splines expansion is used to…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
This paper proposes a penalized composite likelihood method for model selection in colored graphical Gaussian models. The method provides a sparse and symmetry-constrained estimator of the precision matrix, and thus conducts model selection…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful…
Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work,…
Penalized B-splines are routinely used in additive models to describe smooth changes in a response with quantitative covariates. It is typically done through the conditional mean in the exponential family using generalized additive models…
The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…